C4 - ASM question 25

[Crystal Dragon.]

i need help with Q25.10...
[btw -- the poll is just for fun; hoped it would draw attention to the post :)]

Y = {10, 35, 47, 52, 69, 96} (Y-bar = 51)
Y-hat = {8, 32, 48, 60, 72, 86}


i calculated each of the following based on definitions:
ESS = 136 =
RSS = 3966
TSS = 4042

...but now TSS does not equal ESS + RSS.
solution shows ESS = 136 and TSS = 4042, so it looks like my RSS is off, but I can't see how/why.... anybody?

[Oscar]

the problem is with the problem:

mean of Y hat = mean of Y if using the OLS method.
In your case it's not so.

[Abraham Weishaus]

The mean of Y-hat is 51, the same as the mean of Y.

The problem with this problem is that the Y-hats are bogus. There is no set of X's which could possibly lead to these Y-hats being the least squares estimate of the Y's. My intention when posing this problem was to see if you could calculate R^2 without knowing the X's. Nevertheless, I should have used the results of a real regression.

[Retired Bookworm]

I think this problem would fall under the question genre:

"Your co-worker spills coffee all over your work. Can you finish the report with what's left?"

or

"You are a consultant and you are given the following..."

I think the fact that no regression could be made to fit the given data is circumstantial right? After all, it might have been a transformed model (I apologize, I don't have my ASM handy to confirm this technicality could hold). It certainly would be a bad idea to try to derive data to match someone else's results (the word "Audit" comes to mind). The solution would be to know which direction to go once the problem is half solved.

Just a thought. I imagine the SOA would think this way.

No pressure...
:smoke: